ELECTRICAL BREAKDOWN OF THICK ICE LAYERS UNDER IMPULSE VOLTAGE

A. V. Astafurov

(Presented by Professor, Doctor A. A. Vorob’ev)

The paper describes the experimental method and presents volt-time characteristics of river ice for thicknesses of 0.5, 1, and 1.5 cm in uniform and nonuniform electric fields, with exposure durations from \(5 \cdot 10^{-7}\) to \(2 \cdot 10^{-5}\) sec; the rate of discharge development was calculated to be \((2—7) \cdot 10^{-6}\) cm/sec.

Introduction

A substantial shortcoming of the numerous data on the electrical breakdown of solid dielectrics presented in published works is the fact that studies of volt-time characteristics were usually carried out on specimens whose thickness did not exceed 1–2 mm. Apart from the data of Dreger [1], Handrek [2], and Lemhaus [3], who obtained volt-time characteristics for porcelain and glass at thicknesses up to 9 mm, most regularities were obtained on specimens less than 1 mm thick.

It is known that, during breakdown in nonuniform electric fields, as the thickness of the dielectric decreases its electric strength increases, and the polarity effect becomes vanishingly small [4]. The study of volt-second characteristics in the breakdown of solid dielectrics at large thicknesses is of scientific and practical interest.

Comparison of the volt-time characteristics in the breakdown of gaseous, liquid [5, 6], and solid dielectrics will help clarify the physical picture of the electrical breakdown of the latter.

In our experiments, river ice formed under natural conditions was used as the solid dielectric.

As is known, ice has a fairly high electric strength [4]; its crystalline structure is analogous to the structure of wurtzite, in which the positions of the zinc and sulfur atoms are occupied by oxygen atoms held relative to one another by four hydrogen bonds [7].

To determine the composition of the ice, a chemical analysis was carried out. Samples were taken from two pieces of ice. The volume of each sample was 5 l. Each sample was taken from the upper, middle, and lower parts of the ice block. As can be seen from Table 1, the solid residue of the ice at \(110^\circ\)C ranges from 6.2 to 7 mg/l. According to data from the Department of Analytical Chemistry of the Tomsk Polytechnic Institute, the solid residue in once-distilled water is up to 9 mg/l.

Experimental Method

To obtain high-voltage impulses, a 1,440 kV impulse-voltage generator (IVG) was used. To measure the wave amplitude, a capacitive voltage divider and

Table 1

Data from the chemical analysis of three samples of ice-floe waters of the Tom River

Continuation of Table 1

high-voltage electronic oscilloscope with a high recording speed. The oscilloscope had a 13LO2S cathode-ray tube and was manufactured at the Department of High-Voltage Engineering of the Tomsk Polytechnic Institute. For shielding purposes, the electronic oscilloscope was placed in a sheet-iron enclosure 0.8 mm thick. The dimensions of the enclosure were \(1 \times 1.3 \times 1.8\ \text{m}^3\) (Fig. 1).

Synchronization of the impulse-voltage generator (IVG) and the oscilloscope was carried out directly from the oscilloscope spark relay by means of a trigatron (Fig. 2). Successive ignition of the IVG from gap \(G_1\) to gap \(G_7\) was ensured by uniformly increasing the distances between the spheres from 40 mm in the second gap to 70 mm in the last. The selected synchronization circuit fully ensured stable operation of the installation.

For shaping the front of the impulse, five series-connected capacitors of type IM-110, each with a capacitance of 0.025 microfarad (\(C_{\phi}\)), and a resistance \(R_{\phi}\), selected according to the experimental conditions, were used. Changes in \(R_{\phi}\) and \(C_{\phi}\) made it possible to regulate the wave-front length from 1 to 30 microseconds at an amplitude up to 500 kV.

Fig. 1. Metal enclosure for shielding the high-voltage oscilloscope.

Ice specimens for testing had a total thickness of 40--60 mm and were cut out by means of a heated nichrome wire in a direction perpendicular to the free surface of the ice. Figure 3 shows a section of a specimen in the plane of the electrodes; the thickness of the specimens at the breakdown point was 0.5, 1, and 1.5 cm.

The dimensions of the specimen in the plane perpendicular to the direction of breakdown were chosen so as to exclude flashover along the surface. The spherical recess for tests in a uniform electric field was melted out with a heated electrode sphere; the conical recess for tests in a nonuniform field was drilled. Rejection of specimens before testing was carried out visually; those in which dull planes, cracks, or hairline cavities were observed in the region of the electrodes were considered unsuitable. Figure 4 presents a photograph of a specimen 60 mm thick. The clocks were located behind the specimen.

Fig. 2. Circuit diagram of the installation.

In order to prevent flashover along the surface, breakdown was produced in transformer oil at a temperature from \(-15^\circ\) to \(-5^\circ\text{C}\).

In the experiments with ice, polished iron electrodes were used, and in the experiments with distilled water—nickel-plated ones. The spherical electrode had a diameter of 94 mm, and the grounded disk—a plane—80 mm.

The point electrode had a cylindrical-part diameter of 12 mm and a point sharpening angle of about 13°.

Fig. 3. Cross section of specimens for testing in nonuniform (1) and uniform (2) fields.

Fig. 4. Ice plate for preparing a specimen.
The matchbox is in front of the specimen; the watch is behind the specimen.

The specimens were subjected to impulses with amplitudes up to 500 kV. Breakdown occurred on the front of a single impulse.

The voltage impulses were photographed from the screen of a cathode-ray tube with a “Kiev” camera fitted with a “Yupiter” lens of relative aperture 1:2 and a special attachment increasing the focal length in order to obtain a sharp image of the impulse on photographic film. The oscillograms were processed after being enlarged by a factor of 1.5 in comparison with their dimensions on the oscilloscope screen. Panchromatic photographic film of sensitivity 180 GOST units, with emulsion No. 526, developed with ordinary photographic reagents, was used.

Discussion of the results obtained

Figures 5–8 show the dependence of the breakdown voltage on exposure for various thicknesses of river ice; Fig. 9 shows the dependence of the breakdown voltage on thickness; and Fig. 10 shows the dependence of the electric strength \(E_{\mathrm{br}}\) on thickness. The same figures also give, for comparison, analogous dependences obtained by the author,

Fig. 5. Volt-second characteristics of river ice and distilled water. Uniform field, positive-polarity impulse, \(\psi = 90\%\).
— river ice; – – distilled water.

Fig. 6. Volt-second characteristics of river ice and distilled water. Nonuniform field. ●, ○—positive impulse; ▲, △—negative impulse, \(\delta = 0.5\) cm, \(\psi = 90\%\).
1—river ice; 2—distilled water.

for distilled water. At each point, from 7 to 15 specimens were punctured. All curves are plotted from the data of statistical processing of the experimental results at a breakdown probability \(\psi = 90\%\). The scatter of the data amounted to as much as \(\pm 30\text{—}40\%\) of the mean value.

Fig. 7. Volt–second characteristics of river ice and distilled water. Nonuniform field, \(\bullet,\ \circ\)—positive impulse, \(\blacktriangle,\ \triangle\)—negative impulse, \(\delta = 1\ \text{cm}\), \(\psi = 90\%\).
Designation of the curves as in Fig. 6.

Fig. 8. Volt–second characteristics of river ice and distilled water. Nonuniform field; \(\bullet,\ \circ\)—positive impulse, \(\blacktriangle,\ \triangle\)—negative impulse; \(\delta = 1.5\ \text{cm}\), \(\psi = 90\%\).
Designation of the curves as in Fig. 6.

The volt–time characteristics for the breakdown of ice and distilled water in uniform and nonuniform electric fields and for different thicknesses have the form observed for other dielectrics [4, 6]. A significant increase in the electric strength \(E_{\text{br}}\) begins at exposure times of less than \(1\ \mu\text{sec}\). As the thickness of the ice increases, \(E_{\text{br}}\) decreases more rapidly than in distilled water.

Fig. 9. Dependence of the electric strength of river ice and distilled water on thickness at an exposure time of \(1 \cdot 10^{-6}\ \text{sec}\). Nonuniform field; \(\bullet,\ \circ\)—positive impulse; \(\blacktriangle,\ \triangle\)—negative impulse, \(\psi = 90\%\).
Designation of the curves as in Fig. 6.

Fig. 10. Dependence of the breakdown voltage on the thickness of river ice and distilled water at an exposure time of \(1 \cdot 10^{-6}\ \text{sec}\). Nonuniform field, \(\bullet,\ \circ\)—positive impulse; \(\blacktriangle,\ \triangle\)—negative impulse; \(\psi = 90\%\).
Designation of the curves as in Fig. 6.

The volt–time characteristics of ice obtained by us make it possible to calculate the discharge formation time and the velocity of discharge development. The method for determining the discharge formation time, proposed by G. A. Vorob’ev [11], is explained in Fig. 11, where \(U_t\) is the breakdown vol-

voltage at a short exposure; \(U_0\) is the breakdown voltage at which no discharge delay appears; \(t_0\) is the time corresponding to \(U_0\); \(t_{\phi}\) is the discharge formation time; \(t_{\mathrm{sp}}\) is the time of voltage drop upon breakdown of the dielectric.

The determination of the electric strength of non-X-rayed and X-rayed salt at exposures of \(2\cdot 10^{-8}\) sec [8, 9, 11] gave identical values of \(E_{\mathrm{br}}\), which entitles one, in calculating the discharge formation time in solid dielectrics, to neglect the statistical delay time, which is practically absent there owing to the constant presence of free electrons. Applying this last proposition also to ice, according to [10] one can calculate the rate of discharge development by the formula

Fig. 11. Graph for determining the discharge formation time.

\[ v=\frac{\delta}{t_{\phi}}, \]

where \(v\) is the rate of discharge development;
\(\delta\) is the specimen thickness;
\(t_{\phi}\) is the discharge formation time.

Table 2 gives the results of calculations of the formation time and the rate of discharge development in ice.

Comparing the rates of discharge development in ice given in Table 2 with the rates of discharge development in ionic crystals and other dielectrics—

Table 2

Table 3

dielectrics [12], given in Table 3, it may be concluded that the rate of development of the discharge increases with increasing thickness of the solid dielectric. The data given in Tables 2 and 3 on the increase in the discharge velocity with increasing thickness of solid dielectrics are analogous to data on the increase in the velocity of discharge development in a gas gap with increasing length of the latter [5]. This fact makes it possible to suggest the possibility of a streamer character of the discharge in solid dielectrics at large thicknesses.

In our experiments we observed luminescence of ice under the action of high-voltage impulses. Figure 12 presents a photograph of luminescing ice under an impulse voltage of positive polarity with an amplitude of 100 kV, temperature \(-15^\circ\)C. The distance between the electrodes was deliberately greater than the breakdown distance and equal to 70 mm; the specimen was cylindrical in shape, with a cross section of 120 mm and a height of 380 mm; an iron point electrode was frozen into the specimen during its preparation. The specimen was in air. The visible luminescence disappears several seconds after the voltage is removed. The intensity of the luminescence increases as the temperature of the ice is lowered.

Fig. 12. Luminescence of ice in an electric field.

Conclusions

1. The volt-time characteristics of solid and liquid dielectrics in thicknesses from 5 to 15 mm are analogous to the volt-time characteristics of solid and liquid dielectrics at small thicknesses. An increase in the electric strength of ice is observed, as for other solid dielectrics, in the region of short exposures.

2. With increasing thickness of the ice, a decrease in its electric strength is observed.

3. With increasing thickness of the ice, the rate of development of the discharge in it increases.

4. As for ionic crystals [4, 8], a significant increase in the electric strength at negative impulse polarity has been found for ice.

In conclusion, the author expresses sincere gratitude to Professor Doctor A. A. Vorob’ev for suggesting the topic of the work, for scientific guidance, and for his constant interest in the work; to Candidate of Technical Sciences G. A. Vorob’ev for discussion of the work and a number of valuable comments; and also to Senior Lecturer of the Department of Analytical Chemistry V. B. Sokolovich for performing the chemical analysis of the ice.

References

1. Draeger, Arch. f. Elektr., 13, 366, 1924.
2. Handrek, Hescho-Mitt., 46, 1929.
3. Lehmhaus F., Arc. J. Elektr., 32, 281, 1038.
4. Vorob’ev A. A. and Prikhod’ko N. A., Proceedings of the Siberian Physico-Technical Institute, 4, 112, 1936.
5. Edited by Prof. L. I. Sirotinskii, High-Voltage Engineering, Part I, GEI, 1951.
6. Walther A. F. and Inge L. D., ZhFT, 3, 840, 1933.
7. Bokii G. B., Introduction to Crystal Chemistry, Moscow State University, 1954.
8. Walther A. F., Inge L. D., DAN SSSR, 2, 65, 1934.
9. Vorob’ev G. A., ZhETF, 30, 256, 1956.
10. Whitehead S., Breakdown of Solid Dielectrics, GEI, 1957.
11. Vorob’ev G. A., Izv. TPI, 91, 79, 1956.
12. Astafurov A. V., Vorob’ev A. A., Vorob’ev G. A., Kevroleva K. M., Izv. TPI (in the present issue).